United have spent £9m on winger Facundo Pellistri, 18, who joins from Uruguayan side Penarol and has a five-year deal.
Telles has a four-year contract, with the option of a further year.
The 27-year-old, who has one cap for his country, moves to Old Trafford for a fee of 15m euros (£13.6m) plus 2m euros (£1.8m) in add-ons.
Meanwhile, United have agreed to pay 21m euros (£19m) for 18-year-old Diallo with another 20m euros (£18.2m) in add-ons.
The club say he will join “subject to medical, personal terms and work permit”.
They have been monitoring the teenager for the past three years as he came through the ranks at the Italian club.
The Ivorian scored on his Serie A debut in October 2019 and has made three substitute appearances in Italy’s top flight.
Diallo has not featured for Gian Piero Gasperini’s side this season but was the second player born in 2002 to score in one Europe’s top five leagues – England, France, Germany, Italy and Spain – behind Barcelona forward Ansu Fati.
United had been watching 18-year-old Pellistri for a year after being alerted to him by their former striker and ex-Penarol manager Diego Forlan.
“To join a club with the history of Manchester United is a dream come true,” said Pellistri, who has the option of a further year on his deal.
“I have learnt a lot at Penarol and I would like to thank them for everything they have done for me. To have the confidence of the manager is an amazing feeling and I know that working with him will be perfect for my development.
“I am coming into a squad full of great players who I will learn from every day. Everyone knows that Manchester United is a club that gives young players an opportunity and I am ready to work hard every day to earn those chances and prove myself in England.”
Telles ‘a fighter and a winner’
Telles scored 26 goals and made more than 50 assists for Porto after joining them from Galatasaray in 2016.
He said joining United, a club with “prestige”, was a “huge honour”.
“You have to work hard to get to this moment in your career and now I am coming to this club, I can promise that I will give everything in my heart to be a success here,” he added.
“I won many trophies at FC Porto and I want to continue that at United. The manager has a clear plan and direction for this team and I can’t wait to pull on the famous shirt.”
United manager Ole Gunnar Solskjaer said: “First and foremost I welcome Alex to United. He is a player we have been tracking for some time and his performances over the past few years are exactly what we are looking for.
“He is a fighter and a winner and will add real determination and competition to the squad. Alex has the qualities, both as a player and as a person, that we want here at Manchester United.”
Defender Chris Smalling has left the club – completing a permanent move to Roma, where he spent last season on loan.
The England international has signed a three-year deal for a fee of 15m euros (£13.6m), rising to 20m euros (£18.1m) with add-ons.
Smalling played 323 times for United, winning two Premier League titles, one FA Cup, a League Cup and the Europa League.
Amad Diallo is someone they have scouted for quite a long time. He is very inexperienced. He has been at Atalanta for a while but he came over from the Ivory Coast.
He is the kind of player that Manchester United have been building towards signing – a young player that they can develop.
I hesitate to use the name Cristiano Ronaldo but they signed Ronaldo as a relatively young player, he was a little bit more experienced than Diallo but he too was 18 years old.
That is the cultural reboot of United, which the club said they were working towards in the wake of Jose Mourinho’s departure. That is what this kind of signing is aimed at.
Diallo’s signing is more in line [with the cultural reboot] than someone like Edinson Cavani.